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An Improved Upper Bound for the Perturbation Index

  • Ton That Quoc Tan
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Abstract

Let (R,m) be a Noetherian local ring and J be an arbitrary ideal of R. Suppose that f1,…,fr is a J-filter regular sequence in R and I=(f1,…,fr). In this paper, we establish an improved upper bound for the perturbation index of the associated graded ring grJ(R/I), refining the bound obtained by Quy and N. V. Trung.

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Cite

BibTeXRIS
BibTeX
@misc{tan2026improved,
  title = {{An Improved Upper Bound for the Perturbation Index}},
  author = {Ton That Quoc Tan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05299},
  eprint = {2609.05299},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05299},
}
RIS
TY  - UNPB
TI  - An Improved Upper Bound for the Perturbation Index
AU  - Ton That Quoc Tan
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05299
UR  - https://arxiv.org/abs/2609.05299
AB  - Let (R,m) be a Noetherian local ring and J be an arbitrary ideal of R. Suppose that f_1,…,f_r is a J-filter regular sequence in R and I=(f_1,…,f_r). In this paper, we establish an improved upper bound for the perturbation index of the associated graded ring gr_J(R/I), refining the bound obtained by Quy and N. V. Trung.
ER  -